2018/06/11 by Sangjib Kim, Kim, Sangjib, Victor Protsak +1 · 1 citation
Mathematics · #05E10 #05E15 #13A50 #13F50 #20G05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1806.04264
openalex publication_date 2018/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper gives a survey on the relation between Hibi algebras and representation theory. The notion of Hodge algebras or algebras with straightening laws has been proved to be very useful to describe the structure of many important algebras in classical invariant theory and representation theory. In particular, a special type of such algebras introduced by Hibi provides a nice bridge between combinatorics and representation theory of classical groups. We will examine certain poset structures of Young tableaux and affine monoids, Hibi algebras in toric degenerations of flag varieties, and their relations to polynomial representations of the complex general linear group.